Granny is Bayard's grandmother, but Ringo and several other people call her Granny as well. And she fills her role well. She's got white hair and is elderly, and she bakes cookies every Tuesday. Well, not that last part, but she does take good care of the people around her, and herself.
For example, when the boys use improper language ("bastud") when describing how they shot at Union soldiers, she first saves their hides from those same soldiers—then, more importantly, promptly makes them wash out their mouths with soap once the danger has passed.
Even though her morals are very strict, the war and its close calls make her break a lot of her own rules in order to survive. As Bayard hides under her skirts from the Union soldiers, he wonders whether she'll tell a lie to keep the boys safe:
Granny had never whipped us for anything in our lives except lying, and that even when it wasn't a told lie but just keeping quiet, how she would whip us first and then make us kneel down and kneel down with us herself to ask the Lord to forgive us. (1.4.9)
Morals and honesty are obviously pretty important to Granny, but when it comes to survival she's willing to bend or break the truth.
She does, however, have a pretty close relationship with the Lord, given that she's constantly talking to him about her sins and asking for forgiveness. In fact, it's through her prayers that we get a hint as to what she's thinking, even when she does her scamming and stealing. Granny tells God:
"I did not sin for revenge; I defy You or anyone to say I did. I sinned first for justice. And after that first time, I sinned for more than justice: I sinned for the sake of food and clothes for Your own creatures who could not help themselves; for children who had given their fathers, for wives who had given their husbands, for old people who had given their sons, to a holy cause, even though You have seen fit to make it a lost cause." (4.3.25)
Wowser. So Granny sees her "sins" as her part of the great fight against the Union. She sees it as a holy war, so when she steals and shares her proceeds with her neighbors, she finds a way to justify it. Take that, Yanks!
That sharing nature is, in part, what finally does her in. It's not exactly greed that makes her go for the last $1500 against Grumby; it's more a matter of pride:
[S]he had given most of [what she had made] away under the belief that she would be able to replace that and more, but as it was now, she had made independent and secure almost everyone in the county save herself and her own blood;… and how would it be if, when [Father] came home and looked about at his desolate future, she could take fifteen hundred dollars in cash out of her pocket and say, "Here. Start over with this." (4.4.1)
See? Granny isn't looking to make herself rich. In fact, she's taken care of everyone else before herself and her family. What she wants is to show that she has done her part, taking care of the family and the plantation (even though it's burnt to a crisp) throughout the war. The money isn't about power for her; it's a chance for life to go on after the battle. Unfortunately for her, though, she doesn't get to see what life is like when John comes home.